MinT - Best Known (8, 31, s)-Nets in Base 7

Best Known (8, 31, s)-Nets in Base 7

(8, 31, 16)-Net over F₇ — Constructive and digital

Digital (8, 31, 16)-net over F₇, using

net from sequence [i] based on digital (8, 15)-sequence over F₇, using
- Niederreiter sequence [i]

(8, 31, 32)-Net over F₇ — Digital

Digital (8, 31, 32)-net over F₇, using

t-expansion [i] based on digital (7, 31, 32)-net over F₇, using
- net from sequence [i] based on digital (7, 31)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 7 and N(F) ≥ 32, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(8, 31, 158)-Net in Base 7 — Upper bound on s

There is no (8, 31, 159)-net in base 7, because

1 times m-reduction [i] would yield (8, 30, 159)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 23 562044 582950 671347 539135 > 7³⁰ [i]